We already have many of the medicines we need to kill pandemic diseases. But to stop a pandemic itself, we need math.

Statistical analysts and mathematicians can model how a pandemic is likely to unfold across the globe, in many societies - and their work provides the maps for the best systems for stopping the next disease apocalypse. Here are two ways we could prevent pandemics from crippling Homo sapiens, based on mathematical models of disease contagion - and two ways we would only make it worse.

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Patterns of infection

Though a deadly pandemic could come from flu, it might also come from that ancient scourge, the Plague. A mutation in Y. pestis, the Plague-causing bacteria, could leave us vulnerable to one of the deadliest diseases humanity has ever confronted. We might also find ourselves battling SARS, or (less likely) a virus like Ebola that causes extremely deadly and infectious Viral Hemorrhagic Fever.

Regardless of the microbe that threatens us, the pandemic will proceed through eight recognizable stages, from incubation in animals at stage 1, to full pandemic in multiple countries at stage 6 (the peak of the pandemic). The next two stages, post-peak and post-pandemic, are when the disease infects fewer and fewer people until it's gone.

In this classic urban-plague scenario, infected rats (transported, for example, by ships) arrive in a new city and transmit the infection to local house rats and their fleas, which then serve as sources of human infection. Occasionally, humans develop a pneumonic form of plague that is then directly transmitted from human to human through respiratory droplets.

Though Stenseth cautions that modern pandemics don't always bloom first in cities, most pandemic modelers take cities as the fundamental points of contagion – the dots on a map that spawn red lines of infection. But how do you predict where those red lines will go, once they've left the city behind? There's one major difference between the Black Death hitting Paris in the 1340s, and SARS hitting Hong Kong in 2003: Air travel.

Though the SARS outbreak began in mainland China, investigators with the WHO and CDC tracked its global spread to one, isolated incident at Hong Kong's Metropole Hotel. A medical professor visiting from southern China, where SARS had been claiming lives for a few months, checked into a small room on the ninth floor. Within days, 16 guests and visitors to the 9th floor had also come down with the illness – many of them becoming sick after they'd flown to other cities all over the world, from North America to Vietnam. Investigators later came to call it a "superspreading event," and traced it back to a hot zone on the carpet in front of that infected medical professor's hotel room door.

Even three months after the professor had stayed at the hotel, technicians were able to find SARS viruses in the carpet. The World Health Organization (WHO), in its report, speculated that the sick professor might have vomited in front of his room, leaving behind a massive number of live viruses that survived a cleanup from hotel staff. Somehow, those viruses wound up in the lungs of 16 other people who passed near the hotel hot zone, and carried it all over the world – where it nearly became a pandemic.

Incidents like the one in the Metropole Hotel have led pandemic modelers to build air travel routes into nearly all their outbreak scenarios. Tini Garske is a mathematician and researcher with the Imperial College of London's Center for Outbreak Analysis and Modelling, and she's spent most of her career modeling disease outbreak. Her most recent work focuses on generating outbreak scenarios based on Chinese travel patterns. She and her colleagues surveyed 10,000 Chinese from two provinces, looking at typical travel patterns in both rural and urban regions. What they found was that pandemics emerging in rural areas are likely to spread "sufficiently slowly for containment to be feasible," because most people surveyed rarely traveled outside their local areas. But economically developed, urban areas make containment "more difficult" due to the numbers of people traveling great distances on a regular basis.

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It would seem that the answer is just to prevent people from traveling during a pandemic. But by the time we know we're in the midst of a pandemic, it's too late. Many other models show that limiting air travel makes almost no difference when it comes to limiting the spread of disease – at most, it could delay the spread by a week or two. There are, however, a few methods that will probably work – based on models that take Garske's travel research into account, and that incorporate what we learned during the SARS near-pandemic and the H1N1 (swine flu) pandemic of 2009.

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Social distancing

Usually the first idea that comes to mind when we imagine stopping pandemics is quarantine. A quarantine usually means the government separating from the general population people who are known to have been exposed to the disease. Ideally, people who have the disease are isolated both from the general population and the quarantined.

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During the SARS outbreak in Toronto, the Canadian government quarantined people and a number of large public events in Toronto were canceled in the hope that this would contain the disease outbreak in that city. After the dust settled, however, many medical experts, including representatives of the CDC, said that the city had overreacted, quarantining roughly 100 people for every SARS case. York University medical professor Richard Schabas criticized the city of Toronto sharply in a letter to a Canadian journal devoted to infectious disease. "SARS quarantine in Toronto was both inefficient and ineffective. It was massive in scale," he wrote. "An analysis of the efficiency of quarantine in the Beijing outbreak conducted by the American Centers for Disease Control and Prevention concluded that quarantine could have been reduced by two-thirds (four people per SARS case), without compromising effectiveness." In other words, the kinds of mass quarantines you see in virus horror movies like I Am Legend are the worst possible way to stop a pandemic. They burn through health care resources and are ineffective.

If we're facing a brewing pandemic, however, there are good reasons to avoid big social events where the disease could spread. Canceling a large concert, or asking people to stay at home, are both part of a pandemic-containment technique called "social distancing." Most experts say that social distancing and quarantine on a limited basis can help: At UCLA Medical School, biomedical model expert Brian Coburn and his colleagues say school closures and discouraging big public events can reduce the spread of flu by 13 to 17%. Voluntary quarantine in the home seems to work better than closing schools, though closing schools is often a good policy because a microbe's fastest route to pandemic status is to infect children.

From these studies, we can assume that shutting down air travel and instituting widespread quarantine are both methods of dealing with pandemic that will make it worse - by draining resources, creating a false sense of security, and delaying rather than killing the pandemic. So how to we kill the pandemic?

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Vaccination must be global

Let's consider vaccination, which many of us are familiar with from the H1N1 (swine flu) pandemic of 2009. Vaccines program your immune system to recognize and neutralize disease-causing microbes that enter your body. When you get a flu vaccination, you receive a small dose of damaged and dead flu viruses that help your body build up antibodies tailor-made to stop the flu when it shows up. Vaccines are not cures, and don't help people who are already sick. They are only useful as a preventative measure.

Most pandemic modelers agree on one thing: Vaccines stop pandemics in their tracks only if they are administered very early in the outbreak, before the disease has had a chance to spread. Laura Matrajt, a mathematician at the University of Washington in Seattle, has modeled several strategies for containing pandemics with vaccines. The problem, she points out, is that pandemics spread differently depending on the population – as we already saw, a rural outbreak is very different from an urban one. They also spread differently in the developed world than they do in developing countries, largely because children make up nearly 50 percent of the population in many developing countries (in most developed nations children are less than 20 percent of the population).

Vaccinating children is key to stopping a pandemic, because they are what Matrajt a "high-transmission group." In other words, they are humanity's biggest spreaders of disease. If you can vaccinate kids against the pandemic disease, it will spread so much more slowly that you can contain it and protect adults, too. Pandemic modeler Coburn says that some of his colleagues found that "vaccinating 80% of children (less than 19 years old) would be almost as effective as vaccinating 80% of the entire population."

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The problem is that most children are in developing countries that cannot afford to buy vaccines. This is where science butts heads with social reality. Pandemic modelers have to add dark economic truths into their equations, and figure out how best to administer vaccine in a situation where perhaps only two percent of the population will have access to it. Matrajt and her colleagues came up with several scenarios in the developing and developed worlds, where people had access to different amounts of vaccine, ranging from two percent coverage to thirty percent. "For a less developed country, where the high-transmission group accounts for the majority of the population, one needs large amounts of vaccine to indirectly protect the high-risk groups by vaccinating the high-transmission ones," they wrote in a summary of their work.

Here's the upshot: The countries that need the most vaccine the soonest are the least likely to get it.

Though vaccine manufacturers like GlaxoSmithKlein and Sanofi-Aventis have promised to donate millions of vaccines to developing countries, and the WHO can pressure developed nations to donate 10 percent of their stockpiles, these gestures are still woefully inadequate. After contemplating the imbalances in H1N1 vaccine distribution, Dr. Tadataka Yamada with the Bill and Melinda Gates Foundation was so disturbed that he wrote, "I cannot imagine standing by and watching if, at the time of crisis, the rich live and the poor die." With the Foundation, he has published guidelines for the global sharing of vaccine, arguing passionately that "rich countries have a responsibility to stand in line and receive their vaccine allotments alongside poor countries."

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When H1N1 spread far enough that the WHO declared it a pandemic, scientists worked rapidly to synthesize a vaccine and manufacturers churned it out. Still, the vaccine wasn't available until the post-pandemic phase, many months after the pandemic had subsided, and developing countries weren't able to afford as many doses as developed ones. Luckily, this particular strain of the flu was very mild, but the world economic situation is a reminder that vaccine may not be the best weapon against pandemic. If distributed quickly to children in the developing world, vaccines could potentially stop a pandemic before it starts. If not, vaccines can still be used to prevent the deaths of people not yet exposed to the pandemic virus or bacteria.

Decentralized treatment and "hedging"

What about our most obvious strategy? That would be treating the sick with medicines that kill the pandemic disease. In the case of flu, the treatments come from a few antiviral medications. In the case of a new outbreak of the Black Death, we'd look to antibiotics. But we have to ask ourselves the same questions we did when considering how to use vaccines to stop our pandemic. How will we get enough medicine to enough people fast enough?

The answer isn't just to have everybody go to the hospitals. First of all, people may be sick in areas where there are no hospitals, and second during a pandemic hospitals will be overwhelmed with sick people already. Plus, sick people may not actually be able to get out of bed and go to the hospital – especially if everybody in their family is sick too.

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The University of Melbourne's Robert Moss is a vaccine and immunization researcher who points out that we're going to need to come up with some novel ways of delivering antivirals in the event of a pandemic. After researching the ways antivirals were prescribed during the H1N1 pandemic, Moss and his colleagues discovered that medicine wasn't handed out in a timely fashion because of one simple bottleneck: Testing facilities. Most doctors conscientiously sent out blood samples from every person who visited them claiming to have the flu, waiting to hear back from often distant labs for diagnosis. As a result, people went untreated and more cases piled up as labs were overwhelmed. During a more deadly pandemic, the situation would have been disastrous.

Moss says there are a few simple ways that doctors can simplify the process of prescribing medication to avoid this bottleneck. He calls it "decentralization." If a pandemic is underway and labs are overrun, the best way to diagnose patients is just based on the symptoms that they present with. Does it sound like the pandemic disease? Then give them the medicine. There's no time to waste. In addition, Moss recommends setting up informal treatment centers in as many places as possible, including online, to make it easy for people to get diagnosed. Nurses who can't normally prescribe medicines should be allowed to prescribe the antivirals if a patient has the symptoms of the pandemic. And couriers should deliver them to people's houses.

The developing world might be better prepared for this decentralized method than the developed, mainly because many medicines in these countries are given out via decentralized, informal treatment facilities already. Health care workers treating everything from yellow fever to cholera have set up treatment stations in remote regions, hoping to reach the largest number of people.

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University of Hong Kong's Joseph Wu says his models show that countries should always "hedge" by stockpiling two different antiviral medications. That's because viruses often mutate during flu season, becoming resistant to the drugs used to treat it. But if you use two drugs, the virus can't mutate fast enough to keep up. Wu's "hedging" strategy seems to work, at least in computer simulations of outbreaks in urban areas that assume people traveling between cities fairly rapidly. If the city where the outbreak occurs uses two drugs to combat the pandemic instead of one, ten percent fewer people overall will be infected than if only one drug is used. And the number of people infected with mutant strains of the virus will go down from 38 percent, to 2 percent of the population. Those numbers are quite significant, especially because one of our goals as we stop a pandemic is to prevent our microbes from mutating into something we can't treat at all.

As soon as the WHO declares an outbreak, vaccines and at least two different kinds of medicines would be rushed to the regions in the world most affected, to stop the pandemic from spreading. Children should be vaccinated first. If there is no vaccine available, scientists would immediately begin working on synthesizing one. Informal treatment stations would to be set up in any region where there has been an outbreak, so that people can be treated quickly, without bottlenecks. We'd want to avoid big, public gatherings and try to stay home as much as possible. Above all, we'd want coordination between health care workers and pandemic modelers to figure out the best treatment strategy for each area, given the often limited resources we'll have at hand.

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The main thing to remember is that stopping a pandemic isn't about treating individuals – it's about treating groups who are the most likely to spread the pandemic to other people. If your neighbor's child gets a vaccine, that could protect your whole neighborhood more than if you and your adult friends all got them. Likewise, if we can kill a pandemic brewing in a developing country by sharing our vaccines and antivirals, we will save the developed world too.